Uncertainty Analysis of Damage Identification Results Based on Finite Element Model Updating Method

A full-scale seven-story reinforced concrete shear wall building structure was tested on the UCSD-NEES shake table in the period October 2005 January 2006. The shake table tests were designed so as to damage the building progressively through several historical seismic motions reproduced on the shake table. A sensitivitybased finite element (FE) model updating method was used to identify damage in the building. The estimation uncertainty in the damage identification results was observed to be significant, which motivated the authors to perform, through numerical simulation, an uncertainty analysis on a set of damage identification results. This study investigates systematically the performance of FE model updating for damage identification. The damaged structure is simulated numerically through a change in stiffness in selected regions of a FE model of the shear wall test structure. The uncertainty of the identified damage (location and extent) due to variability of five input factors is quantified through effect screening. These five input factors are: (1-3) level of uncertainty in the (identified) modal parameters of each of the first three longitudinal modes, (4) spatial density of measurements (number of sensors), and (5) mesh size in the FE model used in the FE model updating procedure (modeling error). A full factorial design of experiments is considered for these five input factors. The results of this investigation demonstrate that the level of confidence in the damage identification results obtained through FE model updating, is a function of not only the level of uncertainty in the identified modal parameters, but also choices made in the design of experiments (e.g., spatial density of measurements) and modeling errors (e.g., mesh size). Introduction In recent years, structural health monitoring has received increasing attention in the civil engineering research community with the objective to identify structural damage at the earliest possible stage and evaluate the remaining useful life (damage prognosis) of structures. Vibration-based, non-destructive damage identification is based on changes in dynamic characteristics (e.g., modal parameters) of a structure. Experimental modal analysis (EMA) has been used as a technology for identifying modal parameters of a structure based on its measured vibration data. It should be emphasized that the success of damage identification based on EMA depends strongly on the accuracy and completeness of the identified structural dynamic properties. Extensive literature reviews on vibration-based damage identification are provided by Doebling et al. [1, 2] and Sohn et al. [3]. Damage identification consists of (1) detecting the occurrence of damage, (2) localizing the damage zones, and (3) estimating the extent of damage. Numerous vibration-based methods have been proposed to achieve these goals. Salawu [4] presented a review on the use of changes in natural frequencies for damage detection only. However, it is in general impossible to localize damage (i.e., obtain spatial information on the structural damage) from changes in natural frequencies only. Pandey et al. [5] introduced the concept of using curvature mode shapes for damage localization. In their study, by using a cantilever and a simply supported analytical beam model, they demonstrated the effectiveness of employing changes in curvature mode shapes as damage indicator for detecting and localizing damage. Other methods for damage localizations include strain-energy based methods [6] and the direct stiffness calculation method [7]. A class of sophisticated methods consists of applying sensitivity-based finite element (FE) model updating for damage identification [8]. These methods update the physical parameters of a FE model of the structure by minimizing an objective function expressing the discrepancy between numerically predicted and experimentally identified features that are sensitive to damage such as natural frequencies and mode shapes. Optimum solutions of the problem are reached through sensitivitybased optimization algorithms. Recently, sensitivity-based FE model updating techniques have been applied successfully for condition assessment of structures [9]. A full-scale seven-story reinforced concrete (R/C) shear wall building slice was tested on the UCSD-NEES shake table in the period October 2005 January 2006. The shake table tests were designed so as to damage the building progressively through several historical seismic motions reproduced on the shake table. A sensitivitybased FE model updating approach was used to identify damage at each of several damage states of the building based on its identified modal parameters. The estimation uncertainty in both the system identification and damage identification results was observed to be significant [10-13]. This motivated the authors to perform (through numerical simulation) an uncertainty analysis on these system and damage identification results. In an earlier study [14], the authors investigated the performance of three different output-only system identification methods, used for experimental modal analysis of the shear wall building, as a function of the uncertainty/variability in the following input factors: (1) amplitude of input excitation, (2) spatial density of measurements, (3) measurement noise, and (4) length of response data used in the identification process. This paper, which is an extension of the above mentioned study, investigates the performance of damage identification using FE model updating based on the identified modal parameters of the first three longitudinal vibration modes. In this study, the identified modal parameters of the damaged structure are generated numerically using a three-dimensional FE model of the test structure with different levels of damage simulated (numerically) along the height of the structure. The uncertainty of the identified damage (location and extent) is quantified through analysis-of-variance (ANOVA) due to variability of the following input factors: (1-3) level of uncertainty in the (identified) modal parameters of the first three longitudinal modes (M1, M2, M3), (4) spatial density of measurements (number of sensors) (S), and (5) mesh size in the FE model used for damage identification (modeling error) (E). A full factorial design of experiments is considered for these five input factors. Finite Element Model of the Test Structure The full-scale seven-story R/C building slice tested on the UCSD-NEES shake table consists of a main wall (web wall), a back wall perpendicular to the main wall (flange wall) for lateral stability, concrete slabs at each floor level, an auxiliary post-tensioned column to provide torsional stability, and four gravity columns to transfer the weight of the slabs to the shake table. Figure 1 shows a picture of the test structure, a drawing of its elevation, and a rendering of its FE model with fine mesh (one of the two FE models used in this study). Also, a plan view of the structure is presented in Figure 2. Details about construction drawings, material test data, and other information on the set-up and conducting of the experiments are available in [15].